The head of the European Union's humanitarian aid department has warned that the situation in Iraq is deteriorating rapidly while the world is preoccupied with crises elsewhere.

Shortly after Jean-Louis de Brouwer sounded the stark warning, a wave of car bombs targeting public places after nightfall in Baghdad and in a town just south of the Iraqi capital killed a total of 21 people and wounded scores of others.

No group immediately claimed responsibility for the attacks but Baghdad and its surroundings have seen near-daily bombings, mostly targeting the country's majority Shiites or security forces even as authorities struggle to win back territory captured by the Islamic State group.

Earlier in the day, Mr de Brouwer said that the number of displaced people in Iraq has quadrupled in the last year and shows no signs of decreasing.

"The worst is still to come," he said. "The situation is deteriorating, humanitarian aid is becoming even more essential than it was, the problem is funding."

Iraq is convulsed in a battle between the government, its militia allies and forces of the Islamic State group that have taken over large parts of the north and west in the country.

The fighting has displaced some 2.7 million people inside the country, including 110,000 who fled from renewed fighting in and around the city of Ramadi in the western Anbar province in the past two weeks.

Many of these are living with other families, inside mosques or in makeshift camps around the western periphery of Baghdad. Meanwhile, there are hundreds of thousands more in the Kurdish northern regions.

"This is quite a matter for concern as the needs are sky-rocketing and the resources are not increasing," said Mr de Brouwer. "I'm afraid there is also - not donor fatigue - but donor exhaustion."

An even larger refugee problem in neighbouring Syria and the earthquake in Nepal has drawn attention away from the slow building crisis in Iraq, he said.

In June, the EU is to co-host with the UN a new call for humanitarian aid for Iraq in Brussels. .

Mr de Brouwer also criticised the practice of not allowing those displaced from Sunni areas into Baghdad or the Kurdish region without sponsorship, leaving most people stranded.

"If they keep on with this kind of practice, they will end up with the kind of ethnic division that will not be good for the country," he said.

Hours later, a wave of bombings struck Baghdad after nightfall. The deadliest of the attacks hit the western Sunni-majority district of Mansour, killing five people and wounding 12 there, security officials said.

A car bomb near an ice cream shop killed four people and wounded 14 in the Shiite neighbourhood of Hurriya in northern Baghdad. Also, police said two separate car bombs killed a total of seven people and wounded 18 in two Shiite neighbourhoods in eastern Baghdad.

Also, a car bomb exploded near a number of restaurants and shops in Baghdad's eastern Shiite district of Talibiyah, killing two people and wounding 10 others.

And in Madain town just south of Baghdad, a bomb blast near a cafe killed three people and wounded 11.